Power series with positive coefficients arising from the characteristic polynomials of positive matrices

Abstract

Let A be an $$n \times n$$ (entrywise) positive matrix and let $$f(t)=\det (I-t A)$$ . We prove the surprising result that there always exists a positive integer N such that the formal power series expansion of $$1-f(t)^{1/N}$$ around $$t=0$$ has positive coefficients.